Dividing the Pie

In the last post, I suggested that the new version of fairness (C) would make it possible to compare the fairness of different payout schedules for a given format. After a few experiments (and a bit of reflection) later, it’s clear that this will require significantly more work. The assessment of payout schedules must also be informed by the equity considerations that sound in fairness (B).

The innovation in the new fairness (C) measure is in extending it to take account of payouts other than a simple winner-take-all award to the overall champion. This will make it possible to use fairness (C) to judge a wider range of formats, including consolation formats where the open questions arise in parts of the design in which there’s no longer any chance for the player to advance to the ultimate championship. This is, I think, a good thing.

But it’s not going to help assess the fairness of different payout schedules for a given format. The new version of fairness (C), like the old one, is strictly limited to measuring the ability of the tourney to reward superior skill. But if this is the only criterion, the proper payout schedule is obvious. Every dollar you take away from the champion’s payout and give to someone else is going to reduce fairness (C) – you’re putting those dollars into the hands of someone you expect to be less skillful than the champion. So, while its all well and good to have a fairness (C) measure that’s not strictly limited to winner-take-all formats, it’s not going to tell you how to divvy up the prize fund.

Consider the “Odin” tournament described in Follow the Money. That was a 32-player tourney with a prize fund of $10,140. The organizers decided to pay an unusually deep six places, in these amounts: $4,056, $2,028, $2,028, $1,014, $507, and $507. Running the new simulator for 100K trials, the new fairness (C) measure is about 1.76. But revise the payout schedule so that the overall winner received the entire $10,140 and everyone else gets nothing, and fairness (C) is much higher: 17.86 over 100K trials. Giving money to players who are likely to be less skillful than the overall winner causes fairness (C) to tank.

And yet most people, I think, would agree that the payouts that were made are fairer than a winner-take-all payout would have been. That’s because the understanding of fairness is influenced by fairness (B) as well as fairness (C).

The perfect fairness (B) payout would have been to give each of the 32 entrants $316.87. But most people would consider this even payout to be a good deal sillier than the winner-take-all result.

To inform the payout schedule, we need a measure that balances the two aspects of fairness – fairness (B) and fairness (C) – in a way that reflects our intuitive sense of fairness, which includes aspect of both. This will be fairness (D). The new fairness (C) measure is, I think, a necessary step in the right direction – otherwise, we have no fairness (C) measure that deals with multiple payouts. But it’s not, by itself, enough.